The present invention relates to an electron beam drawing apparatus for drawing a circuit pattern or the like on a semiconductor wafer by using an electron beam and a drawing method using an electron beam.
An electron beam drawing apparatus has a great task for improvement in accuracy. Taking several examples, process conditions, proximity effect, blur of an electron beam (error caused by Coulomb effect, an electron beam deflector), accuracy of a mechanism system (positioning accuracy in moving a wafer and a mask) or the like influences on the accuracy.
Among the above-described, the proximity effect is an error caused by whether a drawing pattern is dense or sparse. For example, this is a phenomenon in which in the case of an isolated pattern having a wide interval between patterns with respect to a total of a region of a wafer for drawing, a line width thereof is slender and in the case of a pattern referred to as an overall pattern having a wide area, that is, having a high density with respect to a total of a region, thickening is produced. In recent years, resolution of the above-described problem becomes important owing to a necessity of miniaturization of a line width referred to as design rule for a pattern drawn on a wafer.
As a resolution of a problem in which a pattern is drawn differently from a design value in this way, there is provided an exposure dose determining method for executing proximity effect correction by using an area density map or an exposure dose map disclosed in a literature, F. Murai et al, xe2x80x9cFast proximity effect correction method using a pattern area density mapxe2x80x9d, J. Vac. Sci. Technol. B 10(6) November/December 1992, pp. 3072-3076, Japanese Patent Laid-Open No. 03-225816, Japanese Patent Laid-Open No. 08-213315, Japanese Patent Laid-Open No. 10-229047, U.S. Pat. Nos. 5,149,975 and 5,278,421.
This is a method in which a mesh in a rectangular shape having a certain size is assumed, an area density of a pattern is calculated for each mesh, a map representing a change in the area density of a total of a drawing region is referred to as an area density map or an exposure dose map, and an exposure dose is determined in accordance with the size of the area density to thereby draw the pattern. For example, in the case of the above-described isolated pattern, the area density is small and therefore, the exposure dose is increased whereas in the case of a pattern having a high area density, the exposure dose is reduced.
Further, according to the method, drawing operations of virtual drawing for forming the area density map and actual drawing are carried out. According to the virtual drawing, a calculation is executed up to deflection control of an electron beam with no irradiation on a wafer with the electron beam. Thereby, the area density map is formed and an actual exposure dose is calculated based on data of the area density map to execute actual drawing.
An explanation will be given of the above-described conventional method in reference to FIG. 5 and FIG. 6. FIG. 5 is a functional block diagram representing a constitution of proximity effect correction according to the prior art and FIG. 6 is a flowchart showing its procedure and the explanation will be given as follows.
(1) Drawing for Forming an Area Density Map
(a) Start of Proximity Effect Correction Function
In FIG. 5, there exists data for each shot (a pattern diagram which an actual electron beam can draw by one time exposure) subjected to diagram decomposition (decomposition of pattern data into the pattern which the actual electron beam can draw) at a preceding stage (not illustrated) in an input unit 1 and the following processing is executed for each shot.
(b) Step 1: Start (Input of Data)
Initial shot data is inputted to the input unit 1 in FIG. 5 (block 201 in FIG. 6) and is transmitted to an area density map forming unit 2.
(c) Step 2: Forming an Area Density Map
In the area density map forming unit 2, an area value of a region included in mesh of shot is calculated (block 202 in FIG. 6) and is cumulatively added to an area value of the same mesh (block 203 in FIG. 6). When there is next shot (block 204 in FIG. 6), the next shot is further inputted (block 205 in FIG. 6). The area value of the mesh is previously determined and accordingly, a ratio thereof to the area value of the shot is defined as an area density per mesh. Similar processing is executed for the next shot, the area density per mesh p(x) is calculated, an area density of a total of a drawing reason is mapped and processings of all the shots are finished (block 204 in FIG. 6) and an area density map of the area density p(x) is finished in an area density map memory 3 (block 206 in FIG. 6).
(d) Step 3: Smoothing Processing
Next, the area density map p(x) stored in the area density map memory 3 is read and smoothing is executed for the read map by using a smoothing unit 4 (block 207 in FIG. 6). In this case, the reason of executing smoothing is as follows. Originally, the role of the proximity effect correction resides in executing a correction by simulating back-scattering in which an electron beam is spread in a resist of a wafer by shot and the smoothing unit is a unit for simulating the back-scattering.
Generally, as shown by the above-described literature, the back-scattering can be approximated by a Gaussian distribution and accordingly, the simulation can be carried out by adding a filter such as a Gaussian filter.
After the above-described smoothing operation, the smoothed data is stored again in the area density map memory 3. This operation is repeatedly executed, simulation of the back-scattering is finished (block 208 in FIG. 6) and an area density map constituted by data of the smoothed area density Q0(x) is finished.
(2) Actual Drawing
An exposure dose is calculated based on the area density map of the area density Q0(x) finished in the above-described processing.
(a) Step 4: Start of Actual Drawing (Reading of Data)
Similarly to (1) drawing for forming an area density map, data of the same initial drawing pattern is inputted from the input unit 1 (block 210 in FIG. 6) and is transmitted to the area density map forming unit 2.
(b) Step 5: Area Density Calculation for Each Shot
In the area density map forming unit 2, an address in the area density map memory 3 is calculated, and a value of the area density Q0(x) for each shot is calculated from the area density map memory 3 based on the address (block 211 in FIG. 6).
(c) Step 6: Exposure Dose Conversion Processing
Next, an exposure dose ratio [(1+xcex7)/{1+2xcex7Q0(x)}] for each shot which is a coefficient in consideration of both of forward-scattering energy and back-scattering energy is calculated based on the area density Q0(x) smoothed by simulating the back-scattering (block 212 in FIG. 6). Here, notation xcex7 designates a reflection coefficient representing a ratio of the back-scattering energy to the forward-scattering energy. The reflection coefficient xcex7 is varied by influence of resist or process and accordingly, the reflection coefficient xcex7 must be determined for a material of forming a pattern of a wafer and individual steps.
By using the exposure dose ratio, an exposure dose I(x) for each shot is given by the following equation (1)
I(x)=I50%(x)xc2x7(1+xcex7)/{1+2xcex7Q0(x)}xe2x80x83xe2x80x83(1)
where I50%(x) is an optimum exposure dose with respect to a pattern of 50%.
Further, a value of the calculated exposure dose I(x) is transmitted to an output unit 7 via an exposure amount converting unit 5 and calculation 6 (block 213 in FIG. 6).
When there is next shot (block 214 in FIG. 6), the next shot is further inputted (block 215 in FIG. 6), Step 4 through Step 6 are repeatedly executed and the proximity effect correction is finished by finishing all the shots (block 214 in FIG. 6).
According to the conventional method explained above, an error of a pattern drawn in several xcexcm becomes about several tens nm and the accuracy is sufficient in the case in which the error permitted to the pattern formed on a wafer is about 10%, and poses no problem. However, progress of miniaturization of a circuit pattern of a semiconductor device is fast, in recent years, there are a number of patterns of 0.3 xcexcm or smaller and therefore, the error of about several tens nm becomes problematic. That is, in the case of a pattern of 0.3 xcexcm, the error needs to restrain to 30 nm or smaller and in the case of the pattern of 0.1 xcexcm, the error needs to restrain to about 10 nm.
However, according to the above-described correction method of the prior art using Equation (1), at a portion of the pattern where the pattern density is abruptly changed, the error is caused, and thinning or thickening is produced in a pattern arranged at a vicinity of an edge of a pattern having a high density. The amount of thinning or thickening falls in a range of several nm through several tens nm and will bring about a serious problem in the miniaturization in the future.
As a cause of the above-mentioned problem, it is conceivable that in the above-described prior art the proximity effect correction is constituted by using the approximation (1) derived on the promise that the pattern density is hardly changed in a range of a back-scattering diameter (a magnitude of scattering of an electron beam in a resist of a wafer).
It is an object of the present invention to provide an electron beam drawing apparatus and a drawing method using electron beam capable of reducing a correction error of proximity effect correction without adding a special circuit or a memory and capable of preventing thinning or thickening of a pattern arranged at a vicinity of an edge of a pattern having a high density from being caused.
In order to resolve the above-described object, according to an embodiment of the present invention, correction represented by Equation (1), described above, is reconsidered from a theoretical view point, a method of approximating at a higher order, back-scattering energy and forward-scattering energy is adopted in consideration of a change in a pattern density in a range of a back-scattering diameter and there is adopted a novel proximity effect correcting method adopting a method of determining an exposure dose by modifying an area density thereby.
That is, an embodiment according to the present invention is constructed by a constitution including the steps of dividing the specimen into virtual meshes having a predetermined dimension; calculating an area density of a drawing pattern for each virtual mesh; calculating an area density map of a total of a drawing region of the specimen and storing the area density map in a memory; calculating a modified area density by executing a correction for the area density in consideration of a back-scattering energy and a forward-scattering energy in a resist of the specimen caused by the electron beam to calculate a modified area density; calculating a modified area density map of the total of the drawing region and storing the modified area density map in the memory; and repeating the steps at least twice to determine an exposure dose on the specimen.
Further, another embodiment according to the present invention is constructed by a constitution including the steps of predicting a dimensional deformation caused due to a back-scattering energy and a forward-scattering energy in a resist of a specimen caused by irradiating the drawing pattern to be drawn on the specimen with the electron beam; forming an exposure dose map by calculating an exposure dose of the electron beam used for correcting the dimensional deformation with respect to a total of a drawing region of the specimen; and executing drawing based on the exposure dose map.
Further, still another embodiment according to the present invention is constructed by a constitution including the steps of dividing the specimen into virtual meshes having a predetermined dimension; calculating an area density of the drawing pattern for each virtual mesh; calculating a correction amount of the area density in consideration of a back-scattering energy and a forward-scattering energy in a resist of the specimen caused by the electron beam using a higher order approximation; and determining an exposure dose of the drawing pattern.
Further, further embodiment according to the present invention is constructed by a constitution including the steps of dividing the specimen into virtual meshes having a predetermined dimension; calculating an area density of the drawing pattern for each virtual mesh to form an area density map of a total of a drawing region of the specimen; calculating a first corrected area density by executing a smoothing correction for the area density in consideration of a back-scattering energy and a forward-scattering energy in a resist of the specimen caused by the electron beam to form a first corrected area density map of the total of the drawing region; calculating a modified area density from the first corrected area density and the area density to form a modified area density map of the total of the drawing region; calculating a second corrected area density by performing a smoothing correction for the modified area density in consideration of the back-scattering energy and the forward-scattering energy in the resist of the specimen caused by the electron beam to form a second corrected area density map of the total of the drawing region; calculating an exposure area density from the second corrected area density and the first corrected area density to form an exposure area density map of the total of the drawing region; and calculating an exposure dose for exposing the drawing pattern based on the exposure area density map.
Further, still further embodiment according to the present invention is constructed by a constitution including the steps of calculating an area density of the drawing pattern used for correcting an exposure dose of the electron beam based on a difference from a desired dimension produced by irradiating the drawing pattern drawn on the specimen with the electron beam; calculating an area density map of a total of a drawing region of the specimen and storing the area density map in a memory; and when a pattern contiguous to a line pattern having a linear shape among the drawing patterns drawn on the specimen stays in the middle for its length in a longitudinal direction of the line pattern, determining an exposure dose such that a rate of a change in a width dimension of the line pattern is equal to or smaller than 4% relative to a width dimension of the line pattern at other position before and after the position based on the area density map stored to the memory for drawing.